0
0

Data Interpretation with Percentages

Introduction

In exams, Data Interpretation (DI) problems often use percentages to analyze tables, bar graphs, or pie charts.

These questions test your ability to convert numbers into percentages and compare different categories. Once you know the method, they are straightforward.

Pattern: Data Interpretation with Percentages

Pattern

Percentage = (Part ÷ Whole) × 100

To compare two groups, calculate their percentages and find the difference.

In DI tables/charts, always start with the total, then break down into parts.

Step-by-Step Example

Question

A school has 500 students, out of which 200 are girls and 300 are boys. Find:
1. The percentage of girls in the school.
2. The percentage of boys in the school.

Solution

  1. Step 1: Identify the whole (total students).

    Sentence: Total students = 500

  2. Step 2: Find the percentage of girls.

    Sentence: Girls = 200 out of 500.
    Math: (200 ÷ 500) × 100 = 40%

  3. Step 3: Find the percentage of boys.

    Sentence: Boys = 300 out of 500.
    Math: (300 ÷ 500) × 100 = 60%

  4. Step 4: Final Answer.

    Girls = 40%, Boys = 60%

  5. Step 5: Quick Check.

    40% + 60% = 100% ✅ (matches the total)

Quick Variations

If the question asks: “What % of boys are more than girls?” → Difference ÷ Girls × 100 = (100 ÷ 200) × 100 = 50% more.

If a pie chart shows percentages, multiply total students by that percentage to get the actual number.

Trick to Always Use

  • Step 1: Identify the total (whole).
  • Step 2: Write the part clearly (girls, boys, marks, etc.).
  • Step 3: Apply formula: (Part ÷ Whole) × 100.
  • Step 4: For comparisons, take difference ÷ base × 100.
  • Step 5: Always check if percentages add up to 100%.

Summary

Summary

The Data Interpretation with Percentages pattern uses the simple formula:

Percentage = (Part ÷ Whole) × 100

  • Step 1: Identify total (whole).
  • Step 2: Find percentage of each part.
  • Step 3: Use comparisons if asked.
  • Step 4: Ensure the total adds up logically.

With practice, DI percentage problems become quick and accurate to solve.

Practice

(1/5)
1. A class has 40 students. Out of them, 16 are girls. What percentage of the class are girls?
easy
A. 40%
B. 35%
C. 30%
D. 45%

Solution

  1. Step 1: Identify totals

    Total students = 40, Girls = 16.

  2. Step 2: Compute the percentage

    Percentage = (16 ÷ 40) × 100 = 40%.

  3. Final Answer:

    40% → Option A

  4. Quick Check:

    10% of 40 = 4 → 4 × 4 = 16 ✅
Hint: Compute (part ÷ whole) × 100.
Common Mistakes: Dividing whole by part instead of part by whole.
2. In a survey of 200 people, 80 said they prefer tea. What percentage of people prefer tea?
easy
A. 35%
B. 40%
C. 45%
D. 50%

Solution

  1. Step 1: Identify totals

    Total = 200, Tea lovers = 80.

  2. Step 2: Compute the percentage

    Percentage = (80 ÷ 200) × 100 = 40%.

  3. Final Answer:

    40% → Option B

  4. Quick Check:

    10% of 200 = 20 → 20 × 4 = 80 ✅
Hint: Divide part by whole, then ×100.
Common Mistakes: Omitting ×100 after getting the fraction.
3. In a company of 500 employees, 150 are women. What is the percentage of men?
easy
A. 65%
B. 68%
C. 70%
D. 72%

Solution

  1. Step 1: Compute counts

    Total = 500, Women = 150 → Men = 500 - 150 = 350.

  2. Step 2: Compute the percentage

    Percentage of men = (350 ÷ 500) × 100 = 70%.

  3. Final Answer:

    70% → Option C

  4. Quick Check:

    30% of 500 = 150 → Remaining = 70% ✅
Hint: Find the complement percentage: 100% - women%.
Common Mistakes: Using the count of women directly as percent without conversion.
4. A pie chart shows that 30% of school funds are spent on books. If total funds = ₹50,000, how much is spent on books?
medium
A. 12,000
B. 13,500
C. 14,000
D. 15,000

Solution

  1. Step 1: Identify percentage and total

    Total funds = ₹50,000, Books% = 30%.

  2. Step 2: Compute the amount

    Books expense = (30 ÷ 100) × 50,000 = 15,000.

  3. Final Answer:

    ₹15,000 → Option D

  4. Quick Check:

    10% of 50,000 = 5,000 → 3 × 5,000 = 15,000 ✅
Hint: Use (percentage ÷ 100) × total.
Common Mistakes: Taking percentage of wrong total.
5. In a school of 600 students, 240 play cricket, 180 play football, and the rest play neither. What % play neither?
medium
A. 30%
B. 25%
C. 20%
D. 35%

Solution

  1. Step 1: Sum participants

    Total = 600, Cricket = 240, Football = 180 → Total players = 240 + 180 = 420.

  2. Step 2: Compute neither count

    Neither = 600 - 420 = 180.

  3. Step 3: Compute percentage

    Percentage = (180 ÷ 600) × 100 = 30%.

  4. Final Answer:

    30% → Option A

  5. Quick Check:

    420 + 180 = 600 ✅
Hint: Subtract total participants from whole, then convert to %.
Common Mistakes: Forgetting to add both sport groups before subtracting.

Mock Test

Ready for a challenge?

Take a 10-minute AI-powered test with 10 questions (Easy-Medium-Hard mix) and get instant SWOT analysis of your performance!

10 Questions
5 Minutes